Question

3 what is ( mangle1 )? ( mangle1 = 45^circ ) 4 what are the remaining angle measures? ( mangle2 = 45^circ ), ( mangle3 = 135^circ ), ( mangle4 = 45^circ ) 5 when a transversal intersects parallel lines, corresponding angles are congruent.

Explanation:

Step1: Identify ∠1's corresponding angle

The given 45° angle is corresponding to ∠1, and corresponding angles formed by a transversal cutting parallel lines are congruent.
$m\angle1 = 45^\circ$

Step2: Find ∠2's measure

∠2 is vertical to the 45° angle corresponding to ∠1, and vertical angles are congruent.
$m\angle2 = 45^\circ$

Step3: Find ∠3's measure

∠3 forms a linear pair with ∠2, so they are supplementary (sum to 180°).
$m\angle3 = 180^\circ - 45^\circ = 135^\circ$

Step4: Find ∠4's measure

∠4 is vertical to ∠2, so vertical angles are congruent.
$m\angle4 = 45^\circ$

Answer:

$m\angle1 = 45^\circ$
$m\angle2 = 45^\circ$
$m\angle3 = 135^\circ$
$m\angle4 = 45^\circ$